In the LTE (Long Term Evolution) of the 3GPP (3rd Generation Partnership Project), single-carrier FDMA has been adopted as an uplink wireless access mode (3GPP TS 36.211 V2.0.0, 2007-09, Page 15, paragraph 5.5.1.1). In 3GPP LTE, a reference signal is transmitted for the purpose of estimating CQI (Channel Quality Information) for uplink scheduling or estimating a channel for data demodulation on the reception side.
As such a reference signal, the use of a Zadoff-Chu sequence, which is one CAZAC (Constant Amplitude Zero Auto-Correlation) sequence, is prescribed in 3GPP LTE. In addition, a similar Zadoff-Chu sequence is also used for the preamble signal in random access. Still further, a similar Zadoff-Chu sequence is also used for the reference signal that is transmitted together with the data signal during data channel transmission.
A “CAZAC sequence” here is a sequence having a constant amplitude in both the time domain and frequency domain, and moreover, in which the periodic auto-correlation value is always zero with respect to time shifts other than 0 (zero auto-correlation). A CAZAC sequence is a sequence in which the PAPR (Peak to Average Power Ratio) is suppressed to a low level because it has constant amplitude in the time region, and further, that is suitable for propagation path estimation in the frequency domain due to its constant amplitude in the frequency domain.
The low PAPR as described hereinabove means that power consumption is suppressed to a low level, this feature being a particularly desirable property in mobile communication. Further, the complete auto-correlation characteristic is suited for the detection of the timing of a received signal or the detection of a user signal in random access.
The sequence-defining expression of a Zadoff-Chu sequence that is used as the preamble for a random access channel and that is prescribed in 3GPP LTE is represented by Formula 1:
                                                        X              u                        ⁡                          (              n              )                                =                                    ⅇ                              -                j                                      ⁢                                          π                ⁢                                                                  ⁢                                  un                  ⁡                                      (                    n                    )                                                                              N                zc                                                    ,                                  ⁢                  n          =          0                ,        1        ,        …        ⁢                                  ,                              N            zc                    -          1                                    Formula        ⁢                                  ⁢        1            
Here, u is the sequence number and Nzc is the sequence length. In addition, the value of sequence number u that can be taken is a natural number that is less than the sequence length Nzc, i.e., u=1, . . . , Nzc−1.
Thus, a CAZAC sequence is a sequence-defining expression that includes a quadratic formula relating to n in the numerical expression that is superscript in an exponent.